Pork

To butterfly, put pork loin on a work surface with short end facing you. Holding a long, thin sharp knife parallel to work surface and beginning along one long side, cut 1/2" above underside of roast. Continue slicing inward, pulling back the meat with your free hand and unrolling the roast like a carpet, until the entire loin is flat. Cover with a sheet of plastic wrap. Using a meat mallet, pound to an even thickness.

Uncover pork. Season with 1 tsp. salt and 1/2 tsp. pepper. Place kale leaves on top of loin in an even layer, overlapping as needed and leaving a 1" border. Spread filling on top of kale. Roll pork into a tight cylinder. Wrap one layer of prosciutto around roast. Tie roast securely with kitchen twine in 1" intervals. Tuck rosemary sprigs under twine, spacing apart. DO AHEAD: Pork roast can be made 1 day ahead. Cover and chill. Let stand at room temperature for 1 hour before continuing.

Preheat oven to 400°. Place apples in a roasting pan. Melt 1 Tbsp. butter with oil in a large skillet. Brown pork on all sides, about 5 minutes total, then set on top of apples in pan. Add cider and 1/2 cup water to skillet and bring to a boil, scraping up browned bits. Pour mixture into roasting pan. Roast pork until an instant-read thermometer inserted into center of loin registers 140° (it will be cooked medium but still slightly pink), about 1 hour to 1 hour and 15 minutes. Let roast rest for at least 20 minutes and up to 2 hours.

Put roast on a platter. Reserve apples from roasting pan; spoon off fat from juices in pan. Place pan on top of stove over medium-high heat. Add chicken stock. Pour in reserved mushroom liquid, leaving any sediment behind, and cook, scraping bottom of pan to release any browned bits, until slightly thickened, about 5 minutes. Whisk in remaining 2 Tbsp. butter and season to taste with salt and pepper. Strain sauce; slice pork. Serve sauce and apples alongside sliced pork.